Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, A[100000], len = 0;
  scanf("%d", &n);
  for (int i = 1; (i * (i + 1)) / 2 <= n; i++) {
    A[len++] = (i * (i + 1)) / 2;
  }
  for (int i = 0; i < len; i++) {
    int s = n - A[i];
    if (binary_search(A, A + len, s)) {
      puts("YES");
      return 0;
    }
  }
  puts("NO");
  return 0;
}